Layton Aho | Searcharxiv

arXiv2026

Algorithmic statistics of retinal images

There has been a tremendous amount of image processing and machine learning research to measure and classify disease progression from live optical coherence tomography (OCT) imaging of the retina. The images considered here are large, complex, three-dimensional (3-D) and difficult to visualize effectively. Many current supervised machine learning approaches, \emph{e.g.} neural networks, are non-metric meaning that any features or measurements generated can introduce systematic distortion that may be correlated with underlying non-meaningful physiological differences. Here we present a metric learning approach using the normalized compression distance (NCD) combined with anisotropic structure-enhancing filters to quantify and visualize the principal differences among a collection of 3-D retinal images. We validate the NCD-measured structural differences between pairs of images against the physician-measured change in visual field function, achieving a prediction error of $\sim$ 0.5 dB, more accurate than non-metric deep learning approaches. The normalized compression vectors (NCV) are proposed as a feature set measuring visual differences among a collection of 3-D microscopy images. The utility of the NCV for visualizing and measuring patterns of change is demonstrated for a human with moderate non-progressing glaucoma and for a non-human primate model using intraocular pressure setting manipulation. We conclude with a brief simulation of non-metric embedding features, \emph{e.g.} from neural networks, introducing class-correlated statistical distortion.

eess.IV↗

arXiv2024

A Kolmogorov metric embedding for live cell microscopy signaling patterns

We present a metric embedding that captures spatiotemporal patterns of cell signaling dynamics in 5-D $(x,y,z,channel,time)$ live cell microscopy movies. The embedding uses a metric distance called the normalized information distance (NID) based on Kolmogorov complexity theory, an absolute measure of information content between digital objects. The NID uses statistics of lossless compression to compute a theoretically optimal metric distance between pairs of 5-D movies, requiring no a priori knowledge of expected pattern dynamics, and no training data. The cell signaling structure function (SSF) is defined using a class of metric 3-D image filters that compute at each spatiotemporal cell centroid the voxel intensity configuration of the nucleus w.r.t. the surrounding cytoplasm, or a functional output e.g. velocity. The only parameter is the expected cell radii ($\mu m$). The SSF can be optionally combined with segmentation and tracking algorithms. The resulting lossless compression pipeline represents each 5-D input movie as a single point in a metric embedding space. The utility of a metric embedding follows from Euclidean distance between any points in the embedding space approximating optimally the pattern difference, as measured by the NID, between corresponding pairs of 5-D movies. This is true throughout the embedding space, not only at points corresponding to input images. Examples are shown for synthetic data, for 2-D+time movies of ERK and AKT signaling under different oncogenic mutations in human epithelial (MCF10A) cells, for 3-D MCF10A spheroids under optogenetic manipulation of ERK, and for ERK dynamics during colony differentiation in human stem cells.

cs.CV↗